Introduction to Parametric Optimization and Robustness Evaluation with Optislang

Introduction to parametric optimization and robustness evaluation with optiSLang

Dynardo GmbH

1 © Dynardo GmbH

1. Introduction 2. Process to optiSLang integration

6. Further 3. Sensitivity training analysis

5. Robustness 4. Parametric analysis Optimization

Introduction to the parametric optimization and robustness evaluation with 2 optiSLang © Dynardo GmbH

1. Introduction 2. Process to optiSLang integration

6. Further 3. Sensitivity training analysis

5. Robustness 4. Parametric analysis Optimization

Introduction to the parametric optimization and robustness evaluation with 3 optiSLang © Dynardo GmbH

Excellence of optiSLang

• optiSLang is an algorithmic toolbox for • sensitivity analysis, • optimization, • robustness evaluation, • reliability analysis • robust design optimization (RDO) • functionality of stochastic analysis to run real world industrial applications • advantages: • predefined workflows, • algorithmic wizards and • robust default settings

Introduction to the parametric optimization and robustness evaluation with 4 optiSLang © Dynardo GmbH

Robust Design Optimization (RDO) in virtual product development optiSLang enables you to: • Identify optimization potentials • Improve product performance • Secure resource efficiency • Adjust safety margins without limitation of input parameters • Quantify risks • Save time to market

Introduction to the parametric optimization and robustness evaluation with 5 optiSLang © Dynardo GmbH

Methods for Robust Design Optimization (RDO) with optiSLang

Introduction to the parametric optimization and robustness evaluation with 6 optiSLang © Dynardo GmbH

1. Introduction 2. Process to optiSLang integration

6. Further 3. Sensitivity training analysis

5. Robustness 4. Parametric analysis Optimization

Introduction to the parametric optimization and robustness evaluation with 7 optiSLang © Dynardo GmbH

Process Integration

Parametric model as base for • User defined optimization (design) space • Naturally given robustness (random) space

Design variables Entities that define the design space

Response variables The CAE process Outputs from the Generates the system Scattering variables results according Entities that define the to the inputs robustness space

Introduction to the parametric optimization and robustness evaluation with 8 optiSLang © Dynardo GmbH

Start

Robust Design Optimization

Optimization Robust Design

CAE process (FEM, CFD, Excel, Matlab, etc.)

Introduction to the parametric optimization and robustness evaluation with 9 optiSLang © Dynardo GmbH optiSLang Integrations

Direct integrations

 Matlab

 Excel

 Python

 SimulationX

 Ansys Workbench

Supported connections

 Ansys

 Abaqus

 Adams

 …

Arbitrary connection of ASCII file based solvers

Introduction to the parametric optimization and robustness evaluation with 10 optiSLang © Dynardo GmbH

Full Integration of optiSLang in Ansys Workbench

• optiSLang modules Sensitivity, Optimization and Robustness are directly available in ANSYS Workbench

Introduction to the parametric optimization and robustness evaluation with 11 optiSLang © Dynardo GmbH

Optimization of a tuning fork with optiSLang

• Process integration: Ansys classic (APDL) and Ansys Workbench • Optimization task: How to change a tuning fork so that • Eigen-modes 1, 2 and 3 are 440 Hz, 880 Hz and 1230 Hz each • Mass is max. 80 g Final Design

Introduction to the parametric optimization and robustness evaluation with 12 optiSLang © Dynardo GmbH

Optimization of a tuning fork with optiSLang

Design parameters (here: at DesignModeler)

Rod_Length (40-60 mm)

Rod_Width (5-10 mm)

Radius (7-10 mm)

Depth (5-10 mm)

Grip_Length (20-30 mm)

Grip_Width (4-5 mm)

Introduction to the parametric optimization and robustness evaluation with 13 optiSLang © Dynardo GmbH

Process Integration with optiSLang: tuning fork

Initial Final Design Design

Introduction to the parametric optimization and robustness evaluation with 14 optiSLang © Dynardo GmbH

1. Introduction 2. Process to optiSLang integration

6. Further 3. Sensitivity training analysis

5. Robustness 4. Parametric analysis Optimization

Introduction to the parametric optimization and robustness evaluation with 15 optiSLang © Dynardo GmbH

Flowchart of optiSLang Sensitivity Analysis

Sensitivity analysis

DoE MOP

Solver

• Full design variable space X for sensitivity analysis • Scanning the design space with DoE by direct solver calls • Generating MOP on DoE samples

• Sensitivity analysis gives reduced design variable space Xred • MOP may be used as approximation model for optimization • Best design from DoE as start point may accelerate local optimization

Introduction to the parametric optimization and robustness evaluation with 16 optiSLang © Dynardo GmbH

Scanning the Design Space

Inputs Design of Experiments Solver evaluation Outputs

• Distributions of inputs are represented by Latin Hypercube Sampling • Minimum number of samples should represent statistical properties, cover the input space optimally and avoid clustering • For each design all responses are calculated

Introduction to the parametric optimization and robustness evaluation with 17 optiSLang © Dynardo GmbH

Metamodel of Optimal Prognosis (MOP)

• Approximation of solver output by fast surrogate model • Reduction of input space to get best compromise between available information (samples) and model representation (number of inputs) • Advanced filter technology to obtain candidates of optimal subspace • Determination of optimal approximation model (polynomials, MLS, …) • Assessment of approximation quality (Coefficient of Prognosis, CoP)

MOP algorithm solves 3 important tasks: • Best variable subspace • Best meta-model • Estimation of prediction quality

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Sensitivity Analysis with optiSLang: tuning fork

• Optimization task: Frequency 1 = 440 Hz objectives: Frequency 2 = 880 Hz Frequency 3 = 1320 Hz • Constraints: mass < 80 g

Initial Final Design Design

Introduction to the parametric optimization and robustness evaluation with 19 optiSLang © Dynardo GmbH

1. Introduction 2. Process to optiSLang integration

6. Further 3. Sensitivity training analysis

5. Robustness 4. Parametric analysis Optimization

Introduction to the parametric optimization and robustness evaluation with 20 optiSLang © Dynardo GmbH

Optimization with MOP pre-search

Optimization

Optimizer Optimizer Sensitivity analysis • Gradient • Gradient • ARSM • ARSM DOE MOP • EA/GA • EA/GA

Solver SolverMOP Solver

• Full optimization is performed on MOP by approximating the solver response • Optimal design on MOP can be used as – final design (verification with solver is required!) – as start value for second optimization step with direct solver

• Good approximation quality of MOP is necessary for objective and constraints (CoP ≥ 90%)

Introduction to the parametric optimization and robustness evaluation with 21 optiSLang © Dynardo GmbH

optiSLang Optimization Algorithms

Gradient-based Adaptive Response Nature inspired Methods Surface Method Optimization • Most efficient method if • Attractive method for • GA/EA/PSO imitate gradients are accurate a small set of mechanisms of nature to enough continuous variables improve individuals (<20) • Consider its restrictions • Method of choice if like local optima, only • Adaptive RSM with gradient or ARSM fails continuous variables default settings is the • Very robust against and noise method of choice numerical noise, non- linearity, number of variables,… Start

Introduction to the parametric optimization and robustness evaluation with 22 optiSLang © Dynardo GmbH

Decision Tree for Optimizer Selection

• An optimizer is automatically suggested depending on the parameter properties, the defined criteria as well as user specified settings • Preoptimized reference without failed or noisy solver responses -> NLPQL

Optimization with optiSLang: tuning fork

• Optimization task: Frequency 1 = 440 Hz objectives: Frequency 2 = 880 Hz Frequency 3 = 1320 Hz • Constraints: mass < 80 g

Initial Final Design Design

Initial vs. Optimal Design

Initial Design Optimal Design

Target Design Initial Design Optimal Design Mode 1 [Hz] 440 323 440 Mode 2 [Hz] 880 602 880 Mode 3 [Hz] 1320 1096 1320 Mass [g] < 80 89 54

1. Introduction 2. Process to optiSLang integration

6. Further 3. Sensitivity training analysis

5. Robustness 4. Parametric analysis Optimization

Optimization + Robustness evaluation

Optimization Robustness

Optimizer Robustness Sensitivity analysis • Gradient • Variance • ARSM • Sigma-level DOE MOP • EA/GA • Reliability

Solver Solver Solver

• Full optimization variable space X for sensitivity analysis

• Sensitivity analysis gives reduced optimization variable space Xred

• Optimizer determines optimal design xopt by direct solver calls • Robustness evaluation (varianced-based or reliability-based)

in the random variable space Xrob at optimal design xopt

Robustness Analysis

1) Define the robustness space using 2) Scan the robustness space by scatter range, distribution and producing and evaluating n correlation designs

5) Identify the most 3) Check the variation important scattering 4) Check the variables explainability of the model

Robustness Analysis with optiSLang: tuning fork

Initial Final Design Design

Workflow in optiSLang: tuning fork

Initial Final Design Design

Optimization and Robustness evaluation with optiSLang inside Ansys Workbench

1. Introduction 2. Process to optiSLang integration

6. Further 3. Sensitivity training analysis

5. Robustness 4. Parametric analysis Optimization

Further Training optiSLang 4 Basics 3 day introduction to process integration, sensitivity, optimization, calibration and robustness analysis optiSLang inside ANSYS Workbench 2 day introduction seminar to parameterization in ANSYS Workbench, sensitivity analysis and optimization optiSLang 4 and ANSYS Workbench 1 day introduction to the integration of ANSYS Workbench projects in a optiSLang 4 solver chain, parameterization of signals via APDL output Parameter Identification 1 day seminar on basics of model calibration, application of sensitivity analysis and optimization to calibration problems Robust Design and Reliability Analysis 1 day seminar on basics of probability, robustness and reliability analysis, robust design optimization

See our website: http://www.dynardo.de/en/trainings.html

Thanks for your attention!

Introduction to the parametric optimization and robustness evaluation with 34 optiSLang